Diagram categories and reduced Kronecker coefficients
Roughly speaking, a diagram category is a category whose morphism spaces have bases in terms of certain graphs and composition of morphisms is given by concatenation of graphs. Reduced Kronecker coefficients are stable Kronecker coefficients for the Specht modules for the symmetric group. In this talk, we will discuss mainly two examples of diagram categories, the partition category and the multiparameter colored partition category. We will also review how reduced Kronecker coefficients appear naturally in the representation theory of the partition category. Towards the end of the talk, we will discuss a multiparameter colored version of the partition category and address its relation with representation theory of complex reflection groups of type G(r,1,n). This talk is based on joint work with Volodymyr Mazorchuk.